The Sacramento model is a catchment water balance model that relates runoff to rainfall with daily data. The model contains five stores; and has sixteen parameters.
Scale
Model operates at a functional unit scale and a daily time-step.
Principal developer
Cooperative Research Centre for Catchment Hydrology. The Sacramento model was originally developed for the United States National Weather Service and State of California, Department of Water Resources by Burnash et al. (1973).
Scientific provenance
The Sacramento model has been widely applied in the USA by the National Weather Service. In Australia, the Sacramento model has been the model of choice in water resources studies that have applied the IQQM model and has therefore been very widely applied in Queensland and New South Wales. There have been applications in other Australian states, although these have been fewer in number.
Version
Source v2.10
Source has multiple unit hydrograph values to enable you to redistribute the runoff through time.
Availability/conditions
Sacramento is provided with the Source installer. Sacramento is also available through the Rainfall Runoff Library on eWater Toolkit.
Flow phase
The Sacramento model is a continuous rainfall-runoff model used to generate daily stream flow from rainfall and evaporation records. The conceptual layout of the model is shown in Figure 1.
Figure 1. Sacramento model
 Selecting stream flow data to use in a river-basin-scale simulation study needs information about the reliability of the data. It is best to use data which are most representative of the stream flow from the catchment. Observed data would normally be selected, except where the data are of poor quality or of unknown reliability. |
The Sacramento model uses soil moisture accounting to simulate the water balance within the catchment. Soil moisture storage is increased by rainfall and reduced by evaporation and by flow of water out of the storage. The size and relative wetness of the storage then determines the depth of rainfall absorbed, actual evapotranspiration, and the amount of water moving vertically or laterally out of the store.
Rainfall in excess of that absorbed becomes runoff and is transformed through an empirical unit hydrograph or similar device. Lateral water movements from the soil moisture stores are superimposed on this runoff to give stream flow.
| Equation 1 |  |
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There are five stores in the Sacramento model:
- Upper zone tension water (UZTW);
- Upper zone free water (UZFW);
- Lower zone tension water (LZTW);
- Lower zone primary free water (LZFWP); and
- Lower zone supplementary free water (LZFWS).
The tension water stores represent the volume of water that is held in the soil matrix by surface tension. Water can only be removed from tension stores by evapotranspiration. In the free water stores water can move through the soil vertically to other stores, or laterally as interflow (upper zone) or as base flow (lower zone).
Water movement through the stores is determined by rules, where the UZTW store receives the rain first, and when this is filled water will go to the UZFW store. The UZFW store then supplies water to the lower stores simultaneously, with a user determined split between the free water and tension water stores. When the LZFWS is filled water will go to the tension water stores.
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Stream flow generated with the Sacramento model is made up of three flow components:
- Surface runoff;
- Interflow; and
- Base flow
The generation of these components depends on the amount of water in each store relative to that store’s capacity, and the rate at which water moves into and out of the stores.
Surface runoff is either direct or occurs when UZTWS is full and the rainfall exceeds the sum of the percolation rate and the maximum interflow drainage capacity.
Interflow is generated from the UZFWS as the product of the volume of water in the store, and a drainage rate parameter, UZK.
| Equation 5 |  |
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Base flow is calculated in a similar manner to interflow, using the volume of water in the lower zone free stores with their corresponding drainage rate parameters, LZPK and LZSK. The base flow is then reduced by channel loss parameters, SIDE and SSOUT.
| Equation 6 |  |
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| Equation 7 |  |
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| Equation 9 |  |
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Evapotranspiration can only take place from upper and lower tension water stores and upper free water stores, and directly from the streams. The upper limit of evaporation is the evaporative demand, and is the product of the pan evaporation modified by the (user- specified) pan factor. Evaporation occurs firstly from the UZTWS, then from the UZFWS, and lastly from the LZTWS. Evaporation can also occur directly from the stream as set by SARVA.
Equation 10 |  |
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| Equation 11 |  |
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| Equation 12 |  |
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| Equation 13 |  |
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| Equation 13A |  |
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The percolation to the lower stores is a key process of the Sacramento model. The driving force for percolation is the relative wetness of the UZFWS as moderated by the relative wetness of the lower zone stores.
Percolation increases when either the storage in the UZFW store increases or the storage in the lower zone stores decrease. This is equivalent to supply increasing and demand increasing respectively. Conversely, percolation decreases when the lower stores start becoming full.
The lower limit of percolation, Pbase, occurs when the lower zones are saturated, and is determined by the rate at which the lower zones drain (Equation 14). The maximum rate of percolation occurs when the lower zones are dry, and Pbase is factored up using the ZPERC parameter (Equation 15).
| Equation 14 |  |
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| Equation 15 |  |
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The actual percolation is moderated by the relative saturation of the lower and upper zones, which is the ratio of actual storage to maximum storage in these stores, to give an estimate of percolation (Equation 16).
| Equation 16 |  |
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Normally, the lower zone tension store would fill before water goes to the lower zone free water store. However, variations in soil types cause deviations from average conditions and therefore in the Sacramento model a fraction of the percolation (PFREE) is made available for lower zone free water stores.
| Equation 17 |  |
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| Equation 18 |  |
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| Equation 19 |  |
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| Equation 20 |  |
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| Equation 21 |  |
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Time delay tools
The direct runoff and interflow can be delayed to better represent stream flow hydrographs. The Sacramento model uses a unit hydrograph for this purpose. Each ordinate (UH1...5) represents the proportion of flow which will reach the channel outlet in successive time periods. Sacramento also uses a layered routing process.
Other factors
Other inputs that can also be altered in the calibration process include the parameter RSERV (Fraction of lower zone free water unavailable for transpiration).
Input data
The model requires daily rainfall and potential evapotranspiration data. The rainfall and evaporation data sets need to be continuous (no gaps) and overlapping.
Daily rainfall data may be obtained from rain gauges or rainfall surfaces but will need to be converted to a time series record that is spatially representative of the whole catchment. Note that the time that rainfall data are collected may be important. Very often rainfall data are collected in the morning, the usual time is 9 am, and may be more representative of the previous day’s rainfall. Daily evaporation is an estimate of the spatially averaged evaporation rate of the catchment being modelled. This estimate is subject to the types of land uses that are in the catchment. This may be estimated by applying a crop/land use factor to daily pan or potential evapotranspiration surface data. Daily flow data in ML/day, m3/s or mm/day may be required to calibrate the model. |
Parameters or settings
The Sacramento model uses a total of sixteen parameters to simulate the water balance. Of these:
- five define the size of soil moisture stores;
- three calculate the rate of lateral outflows;
- three calculate the percolation water from the upper to the lower soil moisture stores;
- two calculate direct runoff; and
- three calculate losses in the system
Table 1. Model Parameters
| Parameter | Description | Units | Default | Min | Max |
|---|---|---|---|---|---|
UZTWM | Upper Zone Tension Water Maximum. The maximum volume of water held by the upper zone between field capacity and the wilting point which can be lost by direct evaporation and evapotranspiration from soil surface. This storage is filled before any water in the upper zone is transferred to other storages. | mm | 50 | 0 | 100 |
UZFWM | Upper Zone Free Water Maximum, this storage is the source of water for interflow and the driving force for transferring water to deeper depths. | mm | 40 | 0 | 80 |
LZTWM | Lower Zone Tension Water Maximum, the maximum capacity of lower zone tension water. Water from this store can only be removed through evapotranspiration. | mm | 130 | 0 | 400 |
LZFSM | Lower Zone Free Water Supplemental Maximum, the maximum volume from which supplemental base flow can be drawn. | m | 23 | 0 | 50 |
LZFPM | Lower Zone Free Water Primary Maximum, the maximum capacity from which primary base flow can be drawn. | mm | 40 | 0 | 50 |
UZK | The ratio of water in UZFWM, which drains as interflow each day. | 0.245 | 0.000 | 1.000 | |
LZSK | The ratio of water in LZFSM which drains as base flow each day. | 0.043 | 0 | 1 | |
LZPK | The ratio of water in LZFPM, which drains as base flow each day. | 0.009 | 0 | 1 | |
PFREE | The minimum proportion of percolation from the upper zone to the lower zone directly available for recharging the lower zone free water stores. | 0.063 | 0.000 | 1.000 | |
REXP | An exponent determining the rate of change of the percolation rate with changing lower zone water storage. | 1 | 0 | 3 | |
ZPERC | The factor applied to Pbase to define maximum percolation rate. | 40 | 0 | 80 | |
SIDE | The decimal fraction of observed base flow, which leaves the basin, as groundwater flow. | 0 | 0 | 1 | |
SSOUT | The volume of the flow which can be conveyed by porous material in the bed of stream. | 0.001 | 0.000 | 1.000 | |
PCTIM | The impervious fraction of the basin, and contributes to direct runoff. | 0.01 | 0.00 | 1.00 | |
ADIMP | The additional fraction of pervious area, which develops impervious characteristics under soil saturation, conditions. ADIMP spill only occurs when both tension stores are full. | 0.01 | 0.00 | 1.00 | |
SARVA | A decimal fraction representing that portion of the basin normally covered by streams, lakes and vegetation that can deplete stream flow by evapotranspiration. | 0.01 | 0.00 | 1.00 | |
RSERV | Fraction of lower zone free water unavailable for transpiration | 0.3 | 0.0 | 1.0 | |
UH1 | The first component of the unit hydrograph, ie. the proportion of runoff not lagged | 0.9 | 0 | 1 | |
UH2 | The second component of the unit hydrograph, ie. the proportion of runoff lagged by one time-step | 0.1 | 0 | 1 | |
UH3 | The third component of the unit hydrograph, ie. the proportion of runoff lagged by two time-steps | 0 | 0 | 1 | |
UH4 | The fourth component of the unit hydrograph, ie. the proportion of runoff lagged by three time-steps | 0 | 0 | 1 | |
UH5 | The fifth component of the unit hydrograph, ie. the proportion of runoff lagged by four time-steps | 0 | 0 | 1 |
In Source, up to five unit hydrograph terms (UH1...UH5) can be set to lag the runoff over time. When using RRL v1.0.5 the unit hydrograph term is fixed at 1 for the first time increment, and 0 for the subsequent time increments, and therefore no unit hydrograph routing is applied in RRL. Equivalent behaviour would be achieved with Sacramento in Source by setting UH1 = 1 and UH2 through UH5 to 0. |
The sum of the unit hydrograph terms should always be 1. |
The Sacramento model in Source is configured with a set of default values for each model parameter. There are also upper and lower bounds for each parameter.
As with any modelling, the accuracy and reliability of the results from the Sacramento model are determined by how representative the model is of the catchment (particularly as the Sacramento model is lumped) and also by the quality of the rainfall, evaporation and stream flow data used. The accuracy and reliability of the model can be assessed using the results of comparisons with observed data. As a rule, the calibrated parameter values of a specific catchment should not be transposed to other catchments, unless the reliability of this transposition can be assessed. The parameter set is unique to the climate, topography, size, geology, soil and vegetation type of the catchment on which it was calibrated. There is no proven methodology to adjust these parameters to other catchments, including subcatchments, of the calibrated catchment. |
Output data
The model outputs daily surface and base flow. This may be saved in ML/day, m3/s or mm/day.
Reference list
Burnash, RJC, Ferral, RL & McGuire, RA 1973, A generalized streamflow simulation system: conceptual modeling for digital computers, Technical Report, Joint Federal and State River Forecast Center, US National Weather Service and California Department of Water Resources, Sacramento, CA.
Bibliography
Rainfall Runoff Library v1.0.5, June 25, 2004 (http://www.toolkit.net.au/Tools/RRL).
NOAA Document explaining the conceptualisation of the Sacramento Model.
NOAA version of the soil moisture accounting model (in Fortran).